Question

solve for x. round to the nearest tenth, if necessary.

Explanation:

Step1: Apply the sine function in right - triangle

In right - triangle \( \triangle KLM\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 25^{\circ}\), the side opposite to \(\angle M\) is \(KL = 3.1\), and the hypotenuse is \(KM=x\). So, \(\sin25^{\circ}=\frac{3.1}{x}\).

Step2: Solve for \(x\)

Rearrange the formula \(x=\frac{3.1}{\sin25^{\circ}}\). Since \(\sin25^{\circ}\approx0.4226\), then \(x=\frac{3.1}{0.4226}\approx7.3\).

Answer:

\(x\approx7.3\)